The Push Up is, at its root, a Gymnastic skill; still required to be displayed in every floor routine in the Olympics. It's a fundamental, and it is judged.
As a fitness tool, it's one I see butchered more than most.
Let's start with the basics. Hands about shoulder width apart, fingers & elbows forward. Abs tight, pelvis tucked, butt squeezed.
Lower down until your chest touches the ground with your hands in line with your chest. Press back up to the start position, keeping a flat and tight body position.
Your head stays neutral, in line with your spine. Sounds easy, right? So why is so often butchered?
Over time I've worked with a lot of people that have started with little to no upper body strength. Some get strong, some do not. What sets those that get strong apart from those that do not is staying consistent.
Getting stronger at Push Ups is very simple, it's just not easy.
There are two tools I use for push up strength. Negatives and Assisted. I very, very rarely use knee push ups for anything other than a warm up or as a last resort (someone does not have a sturdy chair or is outside, etc).
In the the video below you will see how to do assisted push ups (at :29).
Start with a high object like a wall or a countertop and work your way down to the floor as you get stronger.
A progression may look like this:
Workout 1: 5 sets of 5 Wall Push Ups, rest :45 between sets
Workout 2: 5 sets of Assisted Push Ups on high countertop, rest :45 between sets
Workout 3: 5 sets of 5 Assisted Push Ups on high countertop, rest :30 between sets
Workout 4: 5 sets of 5 Assisted Push Ups on bed or bench, rest :60 between sets
You would continue in this fashion, lowering your self closer and closer to the floor, while always maintaining tension throughout. This means tight abs and ass, no loosey-goosey.
The other option is one that can be worked in tandem with the assisted push up.
The negative push up starts from a plank position.
Brace yourself (abs and ass) and lower down under control, as slow as possible!
No saggy bottoms, please.
From here you can so a knee push up and return to plank.
Again, 5 sets of 5 will be a good bet. 2-3 sessions a week to start, then as you get stronger try doing lower assisted push ups.
In my gyms we use boxes that are 30, 24, 20, 16, and 12 inches high. From 12" we use stacked bumper plates that allow us to control in 1 inch increments, lower and lower to the floor. The one thing that never waivers is the demand for good form.
Never rush the process. A million sloppy wormies don't equal one real push up.
Be patient, trust the process and get strong! It'll work, I promise.